PID control design and ?? loop shaping

This paper shows that traditional methods for design of PID controllers can be related to robust ℋ︁∞ control. In particular, it shows how the specifications in terms of maximum sensitivity and maximum complementary sensitivity are related to the weighted ℋ︁∞ norm introduced by Glover and McFarlane [5]. The paper also shows how to use the Vinnicombe metric to classify those classes of systems which can be stabilized by the presented design methods in Åström et al [3] and Panagopoulos et al [4].